Given that you are going to apply, the next decision is: Oxford or Cambridge?

There are (at least) two considerations here.

First, the specific course you want to study. Oxford and Cambridge offer (slightly) different courses. If you want to do PPE (Politics, Philosophy and Economics – the course that seemingly every current political adviser has taken) you’ll need to apply to Oxford. Equally, Oxford and Cambridge have different strengths. It can be argued that Cambridge is the best place in the world to study Mathematics (though if you’re going to apply you’d better be certain that you do have a natural gift, rather than being ‘merely’ a bright, hard-worker).

Second, other things being equal, you might consider which of the two places you’d prefer to live in. (Indeed, you might be drawn to a specific college at one or the other.) I personally think that Cambridge is visually more appealing. Oxford colleges tend to be smaller (which you may or may not prefer). There’s no real substitute for actually going there and getting a feel for each place.